Computational investigation for endocytosis of CoVID-19 virus SARS-CoV-2 in cell membrane

CoVID-19 virus SARS-CoV-2 follows the endocytosis process to enter inside a cell to infect it. It is important to study the endocytosis of SARS-CoV-2 in cell membrane to prevent the pandemic of CoVID-19. In this paper we develop a finite element based computational model for endocytosis of SARS-CoV-2 in cell membrane and determine curvature generation on it during the process. The virus SARS-CoV-2 is modeled as a rigid spherical particle and cell membrane as an anisotropic elastic material, while its fluidic nature due to lipid exchange with infinite reservoir is preserved using suitable conditions. With the help of a contact pair created between the virus particle and cell membrane, endocytosis process is computationally studied and the curvature of membrane is evaluated as the time progresses during the endocytosis process. At the tip of the virus particle and half-radius distance from it, the membrane follows the curvature of virus very quickly. However, it takes more time for the membrane point located at a distance equal to the radius of the virus particle. This is compensated by the cytoplasmic peripheral proteins binding onto the inside surface of the cell membrane. The role of cytoplasmic peripheral BAR proteins is investigated by using a linear curvature-coupling model with protein concentrations. It is observed that F-BAR protein is more sensitive to the curvature of virus particle in comparison to the other BAR proteins. The sensitiveness deteriorates as the curvature is increased.

On a consistent rod theory for a linearized anisotropic elastic material: I. Asymptotic reduction method

An asymptotic reduction method is introduced to construct a rod theory for a linearized general anisotropic elastic material for space deformation. The starting point is Taylor expansions about the central line in rectangular coordinates, and the goal is to eliminate the two cross-section spatial variables in order to obtain a closed system for displacement coefficients. This is first achieved, in an ‘asymptotically inconsistent’ way, by deducing the relations between stress coefficients from a Fourier series for the lateral traction condition and the three-dimensional (3D) field equation in a pointwise manner. The closed system consists of 10 vector unknowns, and further refinements through elaborated calculations are performed to extract bending and torsion terms and to obtain recursive relations for the first- and second-order displacement coefficients. Eventually, a system of four asymptotically consistent rod equations for four unknowns (the three components of the central-line displacement and the twist angle) are obtained. Six physically meaningful boundary conditions at each edge are obtained from the edge term in the 3D virtual work principle, and a one-dimensional rod virtual work principle is also deduced from the weak forms of the rod equations.

Asymptotic Field Near the Tip of a Debonded Anticrack in an Anisotropic Elastic Material

Summary We use the sextic Stroh formalism to study the asymptotic elastic field near the tip of a debonded anticrack in a generally anisotropic elastic material under generalised plane strain deformations. The stresses near the tip of the debonded anticrack exhibit the oscillatory singularities $r^{-3/4\pm i\varepsilon }$ and $r^{-1/4\pm i\varepsilon }$ (where $\varepsilon $ is the oscillatory index) as well as the real power-type singularities $r^{-3/4}$ and $r^{-1/4}$. Two complex-valued stress intensity factors and two real-valued stress intensity factors are introduced to respectively scale the two oscillatory and two real power-type singularities. The corresponding three-dimensional analytic vector function is derived explicitly, and the material force on the debonded anticrack is obtained. Our solution is illustrated using an example involving orthotropic materials.

An inverse method for design and characterisation of acoustic materials

This paper presents applications of an inverse method for the design and characterisation of anisotropic elastic material properties of acoustic porous materials. Full field 3D displacements under static surface loads are used as targets in the inverse estimation to fit a material model of an equivalent solid to the measurement data. Test cases of artificial open-cell foams are used, and the accuracy of the results are verified. The method is shown to be able to successfully characterise both isotropic and anisotropic elastic material properties. The paper demonstrates a way to reduce costs by characterising material properties based on the design model without a need for manufacturing and additional experimental tests.

Modeling of the elastic characteristics of a long-fiber reinforced composite with an arbitrary orientation of the reinforcing fibers

Currently, the question of the best scheme for constructing a mathematical model of a homogeneous anisotropic elastic material equivalent to fiber reinforced plastic composite (FRP) with arbitrary laminate stacking sequence configuration, have been remained open. A new method for the theoretical prediction of anisotropic elastic characteristics of material equivalent to a given FRP is suggested in this paper. Results are obtained for representative volume elemen (RV) which has been cut out in three different ways from FRP. Calculations for a specific FRP have shown that the FRP replacement by a homogeneous anisotropic material equivalent to it leads to an error order 10% for the elastic properties.